US10429626B2 - Method for desiging off-axial three-mirror optical system with freeform surfaces - Google Patents
Method for desiging off-axial three-mirror optical system with freeform surfaces Download PDFInfo
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- US10429626B2 US10429626B2 US14/616,463 US201514616463A US10429626B2 US 10429626 B2 US10429626 B2 US 10429626B2 US 201514616463 A US201514616463 A US 201514616463A US 10429626 B2 US10429626 B2 US 10429626B2
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- 238000000034 method Methods 0.000 title claims abstract description 49
- 230000003287 optical effect Effects 0.000 title claims abstract description 42
- 238000004364 calculation method Methods 0.000 claims description 2
- 238000003384 imaging method Methods 0.000 description 2
- 230000004075 alteration Effects 0.000 description 1
- 238000003491 array Methods 0.000 description 1
- 238000010276 construction Methods 0.000 description 1
- 238000005516 engineering process Methods 0.000 description 1
- 238000004519 manufacturing process Methods 0.000 description 1
- 238000005457 optimization Methods 0.000 description 1
- 210000001747 pupil Anatomy 0.000 description 1
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- G—PHYSICS
- G02—OPTICS
- G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
- G02B17/00—Systems with reflecting surfaces, with or without refracting elements
- G02B17/02—Catoptric systems, e.g. image erecting and reversing system
- G02B17/06—Catoptric systems, e.g. image erecting and reversing system using mirrors only, i.e. having only one curved mirror
- G02B17/0626—Catoptric systems, e.g. image erecting and reversing system using mirrors only, i.e. having only one curved mirror using three curved mirrors
- G02B17/0642—Catoptric systems, e.g. image erecting and reversing system using mirrors only, i.e. having only one curved mirror using three curved mirrors off-axis or unobscured systems in which not all of the mirrors share a common axis of rotational symmetry, e.g. at least one of the mirrors is warped, tilted or decentered with respect to the other elements
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- G—PHYSICS
- G02—OPTICS
- G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
- G02B27/00—Optical systems or apparatus not provided for by any of the groups G02B1/00 - G02B26/00, G02B30/00
- G02B27/0012—Optical design, e.g. procedures, algorithms, optimisation routines
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- G06F17/50—
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- G06F17/5086—
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/10—Geometric CAD
- G06F30/17—Mechanical parametric or variational design
Definitions
- the present disclosure relates to a method for designing optical systems, especially a method for designing off-axial three-mirror optical system with freeform surfaces.
- freeform surfaces Compared with conventional rotationally symmetric surfaces, freeform surfaces have higher degrees of freedom, which can reduce the aberrations and simplify the structure of the system in optical design.
- freeform surfaces have been successfully used in the optical field, such as head-mounted-displays, reflective systems, varifocal panoramic optical systems, and micro-lens arrays.
- FIG. 1 is a schematic view of one embodiment of an off-axial three-mirror optical system with freeform surfaces.
- FIG. 2 shows a flow chart of a method for designing off-axial three-mirror optical system with freeform surfaces according to one embodiment.
- FIG. 3 is a schematic view of a selecting method of a plurality of feature rays employed in each field according to one embodiment.
- FIG. 4 is a schematic view of start point and end point of one feature ray while solving the feature data points according to one embodiment.
- FIG. 5 shows a schematic view of an initial system of the off-axial three-mirror optical system with freeform surfaces in FIG. 1 .
- FIG. 6 shows a schematic view of one embodiment of a third freeform surface.
- FIG. 7 shows a schematic view of an off-axial three-mirror optical system with the third freeform surface in FIG. 6 .
- FIG. 8 shows a schematic view of an off-axial three-mirror optical system with three freeform surfaces according to one embodiment.
- FIG. 9 shows a comparison chart of average RMS spot diameter of off-axial three-mirror optical systems with different number of freeform surfaces.
- an off-axial three-mirror optical system with freeform surfaces 10 of one embodiment is provided.
- the off-axial three-mirror optical system with freeform surfaces 10 includes a first freeform surface 1 , a second freeform surface 2 and a third freeform surface 3 , which are separated from each other.
- the second freeform surface 2 is a stop surface. Lights coming from the object space are successively reflected by the first freeform surface 1 , the second freeform surface 2 and the third freeform surface 3 ; and then form an image on an image plane 5 .
- an embodiment of a method for designing the off-axial three-mirror optical system with freeform surfaces includes the following steps:
- step (S 1 ) establishing an initial system, the initial system includes a first initial surface, a second initial surface, and a third initial surface, which are separated from each other;
- step (S 3 ) keeping the third freeform surface 3 and the second initial surface unchanged; and calculating a plurality of second feature data points point by point based on the given object-image relationship and Snell's law to obtain a first freeform surface equation by surface fitting the plurality of second feature data points;
- step (S 4 ) keeping the third freeform surface 3 and the first freeform surface 1 unchanged; and calculating a plurality of third feature data points point by point based on the given object-image relationship and Snell's law to obtain a second freeform surface equation by surface fitting the plurality of third feature data points.
- the first initial surface, the second initial surface and the third initial surface can be planar, spherical, or other surface type.
- a first initial surface location, a second initial surface location and a third initial surface location can be selected according to the optical systems actual needs.
- each of the first initial surface, the second initial surface and the third initial surface is a planar.
- the aperture can be circle, rectangle, square, oval or other shapes.
- six fields are fixed in the construction process; a circular aperture of each of the six fields is divided into fourteen angles with equal intervals; and seven different aperture positions are fixed along the radial direction of each of the fourteen angles. Therefore, 588 different feature rays correspond to different aperture positions and different fields are fixed.
- a surface ⁇ is defined as the unknown freeform surface
- a surface ⁇ ′ is defined as a surface located adjacent to and before the surface ⁇
- a surface ⁇ ′′ is defined as a surface located adjacent to and behind the surface ⁇ .
- a first calculating method includes the following sub-steps:
- Step (d): repeating steps b and c, until all the plurality of first feature data points P i (i 1, 2 . . . K) are calculated.
- step (b) the unit normal vector ⁇ right arrow over (N) ⁇ i (1 ⁇ i ⁇ K ⁇ 1) at each of the feature data point P i (1 ⁇ i ⁇ K ⁇ 1) can be calculated based on the vector form of Snell's Law.
- the unknown freeform surface is a refractive second surface
- r ⁇ i ′ E i ⁇ P i ⁇ ⁇ E i ⁇ P i ⁇ ⁇ is a unit vector along a direction of an exit ray of the unknown freeform surface; and n, n′ is refractive index of a media at two opposite sides of the unknown freeform surface respectively.
- the first calculating method includes a computational complexity formula of
- the first calculating method requires a long computation time.
- a second calculating method includes the following sub-steps:
- Step (f′): repeating steps from b′ to e′, until the plurality of first feature data points P i (i 1, 2 . . . K) are all calculated.
- Step (b′) a calculating method of the unit normal vector ⁇ right arrow over (N) ⁇ i at the ith (1 ⁇ i ⁇ K ⁇ 1) first feature data point P i (1 ⁇ i ⁇ K ⁇ 1) is same as the first calculation method.
- a second calculating method includes a computational complexity formula of
- the computational complexity of the second calculating method is smaller than the computational complexity of the first calculating method.
- constructing the plurality of first feature data points P i (i 1, 2 . . . K) point by point using the second calculating method.
- step (S 3 ) the surface ⁇ is the first freeform surface 1
- the surface ⁇ ′′ is the second freeform surface 2
- Other characteristics of step (S 3 ) are the same as step ( ⁇ ).
- step (S 4 ) the surface ⁇ is the second freeform surface 2
- the surface ⁇ ′′ is the third freeform surface 3 .
- Other characteristics of step (S 4 ) are the same as step ( ⁇ ).
- the off-axial three-mirror optical system with freeform surfaces 10 obtained in one embodiment can be the initial system for further optimization.
- An order of steps (S 1 ) to (S 4 ) can be changed according to the actual needs.
- the initial system was set up with three planes. It can be seen that lights of each field cannot focus on the image plane 5 , and intersections of the lights of each field and the image plane 5 deviate from the ideal image points.
- the third initial surface of the initial system is replaced by the third freeform surface 3 obtained by the above second calculating method. It can be seen that the lights of each field can focus to the ideal image points approximately, which illustrates that the freeform surface, obtained by the designing method, can improve the imaging quality of optical system.
- the first initial surface, the second initial surface and the third initial surface of the initial system are respectively replaced by the first freeform surface 1 , the second freeform surface 2 , and the third freeform surface 3 . It can be seen that the lights of each field can focus to the ideal image points approximately. The image quality can be greatly improved compared to the initial system.
- FIG. 9 is a comparison chart of average RMS spot diameter of off-axial three-mirror optical systems without freeform surface, off-axial three-mirror optical systems with one freeform surface, off-axial three-mirror optical systems with two freeform surfaces, and off-axial three-mirror optical systems with three freeform surfaces. It can be seen that with the increase of the number of freeform surfaces, the average root mean squared (RMS) spot diameter of the off-axial three-mirror optical systems is reduced. The average RMS spot diameter of the off-axial three-mirror optical systems with three freeform surfaces is the smallest, which illustrates that the image quality of the off-axial three-mirror optical systems with three freeform surfaces is the best.
- RMS root mean squared
- the method for designing the off-axial three-mirror optical systems with freeform surfaces can have many advantages.
- each freeform surface of the off-axial three-mirror optical system with freeform surfaces can be generated by a point by point constructing method.
- the method for designing off-axial three-mirror optical system with freeform surfaces is simple and can be applied to various off-axis asymmetric systems.
- the method can be applied in imaging systems with multi-fields and certain aperture, by controlling the feature rays of the multi-fields and different aperture positions, and the number of fields is not limited, thus, the designing method has broad applications.
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- Computer Hardware Design (AREA)
- Evolutionary Computation (AREA)
- General Engineering & Computer Science (AREA)
- Pure & Applied Mathematics (AREA)
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Abstract
Description
is a unit vector along a direction of an incident ray of the unknown freeform surface;
is a unit vector along a direction of an exit ray of the unknown freeform surface; and n, n′ is refractive index of a media at two opposite sides of the unknown freeform surface respectively.
When multi-feature rays are used in a design, the first calculating method requires a long computation time.
When multi-feature rays are used in a design, the computational complexity of the second calculating method is smaller than the computational complexity of the first calculating method. In one embodiment, constructing the plurality of first feature data points Pi (i=1, 2 . . . K) point by point using the second calculating method.
TABLE 1 |
Parameters of the off-axial three-mirror |
optical system with freeform surfaces: |
Parameters | values | ||
FOV | 8° × 9° | ||
Structure | off-axial three-mirror | ||
Wavelength | LWIR(8-12 μm) | ||
entrance pupil diameter | 64 mm | ||
F# | 1.48 | ||
relative aperture(D/f) | 0.676 | ||
focal length (f) | 94.71 mm | ||
Claims (13)
Applications Claiming Priority (3)
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CN201410077992 | 2014-03-05 | ||
CN201410077992.8A CN104898275B (en) | 2014-03-05 | 2014-03-05 | The method for designing of off-axis three reflecting optical system of free form surface |
CN201410077992.8 | 2014-03-05 |
Publications (2)
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US20150253554A1 US20150253554A1 (en) | 2015-09-10 |
US10429626B2 true US10429626B2 (en) | 2019-10-01 |
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US14/616,463 Active 2038-08-03 US10429626B2 (en) | 2014-03-05 | 2015-02-06 | Method for desiging off-axial three-mirror optical system with freeform surfaces |
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CN (1) | CN104898275B (en) |
TW (1) | TWI499796B (en) |
Families Citing this family (13)
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CN105739073B (en) * | 2014-12-11 | 2019-02-12 | 清华大学 | Off-axis three reflecting optical system of free form surface |
CN105467569B (en) * | 2016-01-08 | 2018-03-09 | 苏州大学 | A kind of preposition optical system of off-axis incidence |
CN108152948B (en) * | 2016-12-05 | 2020-02-07 | 清华大学 | Design method of off-axis aspheric optical system |
CN109143558B (en) * | 2018-10-11 | 2023-08-08 | 佛山科学技术学院 | Miniaturized all-weather star sensor optical system |
CN110018566A (en) * | 2019-04-25 | 2019-07-16 | 钟祥博谦信息科技有限公司 | Method, equipment, system and the storage medium of freeform optics system design |
CN110908098B (en) * | 2019-11-11 | 2021-10-01 | 中国科学院上海技术物理研究所 | Large-view-field distortion-eliminating off-axis reflection optical system and design method |
CN113126271B (en) * | 2020-01-15 | 2023-07-28 | 清华大学 | Free-form surface optical telescopic system |
CN114077044A (en) * | 2020-08-14 | 2022-02-22 | 清华大学 | Off-axis two-mirror imaging system |
CN112748569B (en) * | 2020-10-22 | 2022-08-30 | 苏州大学 | Design method of free-form surface reflector in off-axis head-mounted display optical system |
CN114764194B (en) * | 2021-01-15 | 2023-06-06 | 清华大学 | Design method of imaging optical system |
CN114879351A (en) * | 2021-02-05 | 2022-08-09 | 清华大学 | Asymmetrical free-form surface optical system |
CN114035309B (en) * | 2021-11-30 | 2022-07-05 | 东北大学 | Wide-view-field long-wave-band off-axis three-mirror optical system based on free-form surface |
CN117406412B (en) * | 2023-12-14 | 2024-03-08 | 武汉宇熠科技有限公司 | Off-axis reflection type precise measurement optical system based on free curved surface |
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TWI499796B (en) | 2015-09-11 |
US20150253554A1 (en) | 2015-09-10 |
CN104898275B (en) | 2017-07-07 |
CN104898275A (en) | 2015-09-09 |
TW201534964A (en) | 2015-09-16 |
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